You might try flying Southwest from Detroit to LAX for about $250 and then get a flight from LAX to Mendoza on LAN. Try the LAN website and Priceline, expedia, etc... I got my tickets from LAX to MDZ for about $1,100 with taxes and fees etc... Depending on your dates it also looks like flights with AA and LAN are comparable in price if you book directly out of Detroit via one of the online discount sites like priceline, etc...
If you opt for (1) just make sure you have several hours between your Southwest arrival and your LAN departure so that you can pick up your luggage and re-check-in to the international flight.
Another thing to try is checking LAN at various times of day (AM, PM, Graveyard) every day for a couple of weeks straight. I saw fluctuations of over $400 round trip but no apparent pattern. I gambled when they hit like $1200 on LAN, checked Priceline immediately, and got them for about $525 each way + fees.